This disclosure relates to a method for analysis and interpretation of time-series data. More specifically, this disclosure relates to a method for analysis and interpretation of time-series data by determining the singularities of the data. One particular use is in analysis of data, such as acoustic waveforms, from a borehole in a logging operation.
Oil can be found in certain geologic formations at varying depths in the earth's crust. The oil is usually found trapped in layers of porous formations which lies beneath a dome shaped or folded layer of some non-porous rock such as shale. In other instances, oil is trapped at a fault, or break in the layers of the crust.
In the dome and folded formations, natural gas is usually situated between the non-porous layer and the oil described above. The layer beneath the oil is porous and usually is saturated with water. As is well known, oil may be collected by drilling a well. This drilling punctures the reservoir layer and if the penetration is shallow, only natural gas will be collected, if the penetration goes too far, then too much water will be produced. Therefore, it is highly desirable to determine the formation properties at a given depth in the borehole.
Also, the composition of the formation surrounding a borehole may be of interest. Depending on the formation, it may be evident that another area nearby will provide a better return when drilled. Data acquired during logging operations are used to give insight to these materials.
Accurate analysis of acoustic data gathered from a borehole in an oil well is challenging and complex. The field of sonic logging of boreholes involves making acoustic measurements in the borehole at a wide range of frequencies. Acoustic data is generally collected using at least one transmitter and one receiver. There are several different configurations in which borehole acoustic data can be collected. These include cross-well imaging (transmitter in one borehole and receiver in another), borehole seismic (transmitter on the surface and receiver in a borehole), and single-well imaging (transmitter and receiver in the same borehole). Gathering, separating, and analyzing this acoustic data has significant practical applications including fracture identification, compartmentalization, and composition determination.
In order to collect sonic logging data, an acoustic source radiates a compressional wave pulse, which propagates into the surrounding formation. As this pulse enters the formation, it excites compressional and shear waves in the formation. These waves produce head waves in the borehole fluid that may be measured. Also, in their propagation through the formation, the compressional and shear waves encounter interference that results in returning energy back towards the borehole where the receiver may be located. The acoustic responses include head waves and guided borehole waves and Stoneley waves. All of these waves are recorded by the receiver.
The data gathered by the receiver can provide a large amount of information that is highly valuable for the exploration and development of hydrocarbon resources. However, this data must first be accurately analyzed and interpreted. The data retrieved in sonic well logging are extremely complicated because various wave components overlap in time and in frequency or in both domains simultaneously. Unfortunately, standard Fourier transform techniques are not able to discriminate components that overlap in frequency domain, making it difficult to extract information in this case. In order to work around this weakness, conventional systems typically separate frequency spectra to provide low frequency and high frequency analysis. This analysis is useful, but valuable information can be lost due to the overlapping time and frequency components.
Accordingly, it would be desirable to envision a method that would allow analysis of the time series data across a wide range of frequencies, also referred to as a multi-scale analysis. This would allow for a more thorough and informative result that in the instant case could help in analyzing the formation properties surrounding the borehole.
The difficulties and limitations suggested in the preceding are not intended to be exhaustive, but rather are among many which demonstrate that although significant attention has been devoted to increasing the information produced in analyzing time-series data, specifically acoustic data, prior attempts do not satisfy the need for analysis of data across a wide range of frequencies.